Any semiclassical computation in quantum field theory in curved spacetime faces two main issues: the presence of ultraviolet divergences and the inexistent of a unique criteria to select a vacuum state [1]}, [2]}, [3]}, [4]}. The former makes the computation of the stress-energy tensor or the two point function a non-trivial issue even at the vacuum level. In order to obtain physical finite observables we need to make use of a regularization and renormalization scheme. For the particular case of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes, adiabatic regularization [5]} fixes all the subtraction terms that are needed to be added to the original divergent term of the above mentioned bilinears. This regularization scheme serves for both scalar [5]} and Dirac fields [7]}, even in interacting theories with an electromagnetic field [8]}, [9]}, [10]} and a classical scalar field [11]}, [12]}, [13]}, [9]}. In the latter, it is assumed a Yukawa interaction between the background scalar field and the quantized scalar or Dirac fields.
